mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-30 00:50:37 +08:00
Tal Ben-Nun
4f049db7c2
This method numerically computes function derivatives in different scales, extrapolating between intermediate results to conserve function evaluations. Adaptive differentiation is essential to produce accurate results for functions with noisy derivatives. Full changelist: -Created a new type of NumericDiffMethod (RIDDERS). -Implemented EvaluateRiddersJacobianColumn in NumericDiff. -Created unit tests with f(x) = x^2 + [random noise] and f(x) = exp(x). Change-Id: I2d6e924d7ff686650272f29a8c981351e6f72091
359 lines
15 KiB
C++
359 lines
15 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
|
|
// Copyright 2015 Google Inc. All rights reserved.
|
|
// http://ceres-solver.org/
|
|
//
|
|
// Redistribution and use in source and binary forms, with or without
|
|
// modification, are permitted provided that the following conditions are met:
|
|
//
|
|
// * Redistributions of source code must retain the above copyright notice,
|
|
// this list of conditions and the following disclaimer.
|
|
// * Redistributions in binary form must reproduce the above copyright notice,
|
|
// this list of conditions and the following disclaimer in the documentation
|
|
// and/or other materials provided with the distribution.
|
|
// * Neither the name of Google Inc. nor the names of its contributors may be
|
|
// used to endorse or promote products derived from this software without
|
|
// specific prior written permission.
|
|
//
|
|
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
|
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
|
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
|
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
|
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
|
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
|
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
|
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|
// POSSIBILITY OF SUCH DAMAGE.
|
|
//
|
|
// Author: keir@google.com (Keir Mierle)
|
|
// tbennun@gmail.com (Tal Ben-Nun)
|
|
|
|
#include "ceres/numeric_diff_cost_function.h"
|
|
|
|
#include <algorithm>
|
|
#include <cmath>
|
|
#include <string>
|
|
#include <vector>
|
|
#include "ceres/internal/macros.h"
|
|
#include "ceres/internal/scoped_ptr.h"
|
|
#include "ceres/numeric_diff_test_utils.h"
|
|
#include "ceres/test_util.h"
|
|
#include "ceres/types.h"
|
|
#include "glog/logging.h"
|
|
#include "gtest/gtest.h"
|
|
|
|
namespace ceres {
|
|
namespace internal {
|
|
|
|
TEST(NumericDiffCostFunction, EasyCaseFunctorCentralDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor,
|
|
CENTRAL,
|
|
3, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new EasyFunctor));
|
|
EasyFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, EasyCaseFunctorForwardDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor,
|
|
FORWARD,
|
|
3, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new EasyFunctor));
|
|
EasyFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, EasyCaseFunctorRidders) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor,
|
|
RIDDERS,
|
|
3, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new EasyFunctor));
|
|
EasyFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, EasyCaseCostFunctionCentralDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyCostFunction,
|
|
CENTRAL,
|
|
3, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new EasyCostFunction, TAKE_OWNERSHIP));
|
|
EasyFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, EasyCaseCostFunctionForwardDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyCostFunction,
|
|
FORWARD,
|
|
3, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new EasyCostFunction, TAKE_OWNERSHIP));
|
|
EasyFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, EasyCaseCostFunctionRidders) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyCostFunction,
|
|
RIDDERS,
|
|
3, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new EasyCostFunction, TAKE_OWNERSHIP));
|
|
EasyFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction,
|
|
TranscendentalCaseFunctorCentralDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<TranscendentalFunctor,
|
|
CENTRAL,
|
|
2, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new TranscendentalFunctor));
|
|
TranscendentalFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction,
|
|
TranscendentalCaseFunctorForwardDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<TranscendentalFunctor,
|
|
FORWARD,
|
|
2, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new TranscendentalFunctor));
|
|
TranscendentalFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction,
|
|
TranscendentalCaseFunctorRidders) {
|
|
NumericDiffOptions options;
|
|
|
|
// Using a smaller initial step size to overcome oscillatory function
|
|
// behavior.
|
|
options.ridders_relative_initial_step_size = 1e-3;
|
|
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<TranscendentalFunctor,
|
|
RIDDERS,
|
|
2, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new TranscendentalFunctor, TAKE_OWNERSHIP, 2, options));
|
|
TranscendentalFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction,
|
|
TranscendentalCaseCostFunctionCentralDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<TranscendentalCostFunction,
|
|
CENTRAL,
|
|
2, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new TranscendentalCostFunction, TAKE_OWNERSHIP));
|
|
TranscendentalFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction,
|
|
TranscendentalCaseCostFunctionForwardDifferences) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<TranscendentalCostFunction,
|
|
FORWARD,
|
|
2, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new TranscendentalCostFunction, TAKE_OWNERSHIP));
|
|
TranscendentalFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction,
|
|
TranscendentalCaseCostFunctionRidders) {
|
|
NumericDiffOptions options;
|
|
|
|
// Using a smaller initial step size to overcome oscillatory function
|
|
// behavior.
|
|
options.ridders_relative_initial_step_size = 1e-3;
|
|
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<TranscendentalCostFunction,
|
|
RIDDERS,
|
|
2, /* number of residuals */
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new TranscendentalCostFunction, TAKE_OWNERSHIP, 2, options));
|
|
TranscendentalFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
|
|
}
|
|
|
|
template<int num_rows, int num_cols>
|
|
class SizeTestingCostFunction : public SizedCostFunction<num_rows, num_cols> {
|
|
public:
|
|
virtual bool Evaluate(double const* const* parameters,
|
|
double* residuals,
|
|
double** jacobians) const {
|
|
return true;
|
|
}
|
|
};
|
|
|
|
// As described in
|
|
// http://forum.kde.org/viewtopic.php?f=74&t=98536#p210774
|
|
// Eigen3 has restrictions on the Row/Column major storage of vectors,
|
|
// depending on their dimensions. This test ensures that the correct
|
|
// templates are instantiated for various shapes of the Jacobian
|
|
// matrix.
|
|
TEST(NumericDiffCostFunction, EigenRowMajorColMajorTest) {
|
|
scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<SizeTestingCostFunction<1,1>, CENTRAL, 1, 1>(
|
|
new SizeTestingCostFunction<1,1>, ceres::TAKE_OWNERSHIP));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<SizeTestingCostFunction<2,1>, CENTRAL, 2, 1>(
|
|
new SizeTestingCostFunction<2,1>, ceres::TAKE_OWNERSHIP));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<SizeTestingCostFunction<1,2>, CENTRAL, 1, 2>(
|
|
new SizeTestingCostFunction<1,2>, ceres::TAKE_OWNERSHIP));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<SizeTestingCostFunction<2,2>, CENTRAL, 2, 2>(
|
|
new SizeTestingCostFunction<2,2>, ceres::TAKE_OWNERSHIP));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 1>(
|
|
new EasyFunctor, TAKE_OWNERSHIP, 1));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 1>(
|
|
new EasyFunctor, TAKE_OWNERSHIP, 2));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 2>(
|
|
new EasyFunctor, TAKE_OWNERSHIP, 1));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 1, 2>(
|
|
new EasyFunctor, TAKE_OWNERSHIP, 2));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 2, 1>(
|
|
new EasyFunctor, TAKE_OWNERSHIP, 1));
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor, CENTRAL, ceres::DYNAMIC, 2, 1>(
|
|
new EasyFunctor, TAKE_OWNERSHIP, 2));
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction,
|
|
EasyCaseFunctorCentralDifferencesAndDynamicNumResiduals) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<EasyFunctor,
|
|
CENTRAL,
|
|
ceres::DYNAMIC,
|
|
5, /* size of x1 */
|
|
5 /* size of x2 */>(
|
|
new EasyFunctor, TAKE_OWNERSHIP, 3));
|
|
EasyFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, ExponentialFunctorRidders) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<ExponentialFunctor,
|
|
RIDDERS,
|
|
1, /* number of residuals */
|
|
1 /* size of x1 */>(
|
|
new ExponentialFunctor));
|
|
ExponentialFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, ExponentialCostFunctionRidders) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<ExponentialCostFunction,
|
|
RIDDERS,
|
|
1, /* number of residuals */
|
|
1 /* size of x1 */>(
|
|
new ExponentialCostFunction));
|
|
ExponentialFunctor functor;
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, RandomizedFunctorRidders) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
NumericDiffOptions options;
|
|
// Larger initial step size is chosen to produce robust results in the
|
|
// presence of random noise.
|
|
options.ridders_relative_initial_step_size = 10.0;
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<RandomizedFunctor,
|
|
RIDDERS,
|
|
1, /* number of residuals */
|
|
1 /* size of x1 */>(
|
|
new RandomizedFunctor(kNoiseFactor, kRandomSeed), TAKE_OWNERSHIP,
|
|
1, options));
|
|
RandomizedFunctor functor (kNoiseFactor, kRandomSeed);
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
|
|
}
|
|
|
|
TEST(NumericDiffCostFunction, RandomizedCostFunctionRidders) {
|
|
internal::scoped_ptr<CostFunction> cost_function;
|
|
NumericDiffOptions options;
|
|
// Larger initial step size is chosen to produce robust results in the
|
|
// presence of random noise.
|
|
options.ridders_relative_initial_step_size = 10.0;
|
|
|
|
cost_function.reset(
|
|
new NumericDiffCostFunction<RandomizedCostFunction,
|
|
RIDDERS,
|
|
1, /* number of residuals */
|
|
1 /* size of x1 */>(
|
|
new RandomizedCostFunction(kNoiseFactor, kRandomSeed),
|
|
TAKE_OWNERSHIP, 1, options));
|
|
RandomizedFunctor functor (kNoiseFactor, kRandomSeed);
|
|
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
|
|
}
|
|
|
|
|
|
} // namespace internal
|
|
} // namespace ceres
|